Question

Write each number in the appropriate box to show its placement along the number line. 0.21, 3/11, -2 1/6, 2.375, -1.62, 2 2/9, 5/3, -1.26.

Answer 1

Number line

We know that the placement along the number line is given by the how big are the numbers placed.

If a number is higher than the other it is at its right. If a number is lower than the other, then it is at its left.

Given the numbers:

0.21, 3/11, -2 1/6, 2.375, -1.62, 2 2/9, 5/3, -1.26.​

we are going to organize them from the smaller one to the highest so we can organize them.

Step 1

Using the calculator, we are going to find the decimal value for the fractions:

`\begin{gathered} (3)/(11)\approx0.27 \\ -2(1)/(6)=(-2*6)/(6)+(1)/(6)=-(12)/(6)+(1)/(6)=-(11)/(6)\approx-1.83 \\ 2(2)/(9)=(2*9)/(9)+(2)/(9)=(18)/(9)+(2)/(9)=(20)/(9)\approx2.22 \\ (5)/(3)\approx1.67 \end{gathered}`

Then, using those decimal values, we have the following list of numbers:

0.21, 3/11, -2 1/6, 2.375, -1.62, 2 2/9, 5/3, -1.26.​

↓

0.21, 0.27, -1.83, 2.375, -1.62, 2.22, 1.67, -1.26.​

Step 2

Now, we want to organize them from the lowest to the highest:

0.21, 0.27, -1.83, 2.375, -1.62, 2.22, 1.67, -1.26.​

↓

-1.83 = -2 1/6

-1.62

-1.26

0.21,

0.27 = 3/11

1.67 = 5/3

2.22 = 2 2/9

2.375

Now, we can locate them

Step 3

Locating them in that order:

↓ using the original fractions